Koscielny had a year remaining on his contract in North London but was adamant to return to his home country after nine years away.
The 33-year-old tried to engineer a free transfer from the club but Arsenal held firm in their desire to retain his services for the upcoming season.
Koscielny subsequently failed to show up for the club’s pre-season tour of the United States in a bid to force a move away.
A statement on the Gunners’ official website read: “The centre back has made 353 appearances for us since signing from Lorient in 2010. He was part of our Emirates FA Cup-winning squads in 2014, 2015 and 2017.
“Laurent, who started his career in the French second division at Guingamp in 2004, has played 51 matches for France and was entering the final year of his current contract with us. We decided to sanction his move to Bordeaux once we agreed acceptable transfer terms.
“We thank Laurent for his contribution to the club and wish him all the best for the future.
“The transfer is subject to the completion of regulatory processes.”
Koscielny missed a chunk of the first half of last season through a raptured Achilles injury suffered in May 2018 that saw him sit out the World Cup in Russia but he still made 29 appearances in all competitions for Arsenal after returning to action in December.
Arsenal manager Unai Emery is already seeking a replacement for the veteran as the transfer window approaches its closure on Thursday.
